263,646 research outputs found
Weak Values and Consistent Histories in Quantum Theory
A relation is obtained between weak values of quantum observables and the
consistency criterion for histories of quantum events. It is shown that
``strange'' weak values for projection operators (such as values less than
zero) always correspond to inconsistent families of histories. It is argued
that using the ABL rule to obtain probabilities for counterfactual measurements
corresponding to those strange weak values gives inconsistent results. This
problem is shown to be remedied by using the conditional weight, or
pseudo-probability, obtained from the multiple-time application of Luders'
Rule. It is argued that an assumption of reverse causality (a form of time
symmetry) implies that weak values obtain, in a restricted sense, at the time
of the weak measurement as well as at the time of post-selection. Finally, it
is argued that weak values are more appropriately characterised as
multiple-time amplitudes than expectation values, and as such can have little
to say about counterfactual questions.Comment: Final version, to appear in Studies in History and Philosophy of
Modern Physic
Triaxial Galaxies with Cusps
We have constructed fully self-consistent models of triaxial galaxies with
central density cusps. The triaxial generalizations of Dehnen's spherical
models are presented, which have densities that vary as 1/r^gamma near the
center and 1/r^4 at large radii. We computed libraries of about 7000 orbits in
each of two triaxial models with gamma=1 (weak cusp) and gamma=2 (strong cusp);
these two models have density profiles similar to those of the core and
power-law galaxies observed by HST. Both mass models have short-to-long axis
ratios of 1:2 and are maximally triaxial. A large fraction of the orbits in
both model potentials are stochastic, as evidenced by their non-zero Liapunov
exponents. We show that most of the stochastic orbits in the strong- cusp
potential diffuse relatively quickly through their allowed phase-space volumes,
on time scales of 100 - 1000 dynamical times. Stochastic orbits in the
weak-cusp potential diffuse more slowly, often retaining their box-like shapes
for 1000 dynamical times or longer. Attempts to construct self- consistent
solutions using just the regular orbits failed for both mass models.
Quasi-equilibrium solutions that include the stochastic orbits exist for both
models; however, real galaxies constructed in this way would evolve near the
center due to the continued mixing of the stochastic orbits. We attempted to
construct more nearly stationary models in which stochastic phase space was
uniformly populated at low energies. These ``fully mixed'' solutions were found
to exist only for the weak-cusp potential. No significant fraction of the mass
could be placed on fully-mixed stochastic orbits in the strong-cusp model,
demonstrating that strong triaxiality can be inconsistent with a high central
density.Comment: 58 TEX pages, 14 PostScript figures, uses epsf.st
Unsupervised Object Discovery and Tracking in Video Collections
This paper addresses the problem of automatically localizing dominant objects
as spatio-temporal tubes in a noisy collection of videos with minimal or even
no supervision. We formulate the problem as a combination of two complementary
processes: discovery and tracking. The first one establishes correspondences
between prominent regions across videos, and the second one associates
successive similar object regions within the same video. Interestingly, our
algorithm also discovers the implicit topology of frames associated with
instances of the same object class across different videos, a role normally
left to supervisory information in the form of class labels in conventional
image and video understanding methods. Indeed, as demonstrated by our
experiments, our method can handle video collections featuring multiple object
classes, and substantially outperforms the state of the art in colocalization,
even though it tackles a broader problem with much less supervision
Lopsidedness of self-consistent galaxies by the external field effect of clusters
Adopting Schwarzschild's orbit-superposition technique, we construct a series
of self-consistent galaxy models, embedded in the external field of galaxy
clusters in the framework of Milgrom's MOdified Newtonian Dynamics. These
models represent relatively massive ellipticals with a Hernquist radial profile
at various distances from the cluster centre. Using -body simulations, we
perform a first analysis of these models and their evolution. We find that
self-gravitating axisymmetric density models, even under a weak external field,
lose their symmetry by instability and generally evolve to triaxial
configurations. A kinematic analysis suggests that the instability originates
from both box and non-classified orbits with low angular momentum. We also
consider a self-consistent isolated system which is then placed in a strong
external field and allowed to evolve freely. This model, just as the
corresponding equilibrium model in the same external field, eventually settles
to a triaxial equilibrium as well, but has a higher velocity radial anisotropy
and is rounder. The presence of an external field in MOND universe generically
predicts some lopsidedness of galaxy shapes.Comment: 24 pages, 20 figures. Accepted for publication in Ap
Integrated cosmological probes: Concordance quantified
Assessing the consistency of parameter constraints derived from different
cosmological probes is an important way to test the validity of the underlying
cosmological model. In an earlier work [Nicola et al., 2017], we computed
constraints on cosmological parameters for CDM from an integrated
analysis of CMB temperature anisotropies and CMB lensing from Planck, galaxy
clustering and weak lensing from SDSS, weak lensing from DES SV as well as Type
Ia supernovae and Hubble parameter measurements. In this work, we extend this
analysis and quantify the concordance between the derived constraints and those
derived by the Planck Collaboration as well as WMAP9, SPT and ACT. As a measure
for consistency, we use the Surprise statistic [Seehars et al., 2014], which is
based on the relative entropy. In the framework of a flat CDM
cosmological model, we find all data sets to be consistent with one another at
a level of less than 1. We highlight that the relative entropy is
sensitive to inconsistencies in the models that are used in different parts of
the analysis. In particular, inconsistent assumptions for the neutrino mass
break its invariance on the parameter choice. When consistent model assumptions
are used, the data sets considered in this work all agree with each other and
CDM, without evidence for tensions.Comment: 17 pages, 4 figures, 2 tables, updated following referee's comments,
now includes discussion of the Riess et al., 2016 Hubble parameter
measurement, matches version accepted by JCA
EPR before EPR: a 1930 Einstein-Bohr thought experiment revisited
In 1930 Einstein argued against consistency of the time-energy uncertainty
relation by discussing a thought experiment involving a measurement of mass of
the box which emitted a photon. Bohr seemingly triumphed over Einstein by
arguing that the Einstein's own general theory of relativity saves the
consistency of quantum mechanics. We revisit this thought experiment from a
modern point of view at a level suitable for undergraduate readership and find
that neither Einstein nor Bohr was right. Instead, this thought experiment
should be thought of as an early example of a system demonstrating nonlocal
"EPR" quantum correlations, five years before the famous
Einstein-Podolsky-Rosen paper.Comment: 11 pages, revised, accepted for publication in Eur. J. Phy
Square compactness and the filter extension property
We show that the consistency strength of κ being 2κ-square compact is at least weak compact and strictly less than indescribable. This is the first known improvement to the upper bound of strong compactness obtained in 1973 by Hajnal and Juhasz
Statistical tests of sterile neutrinos using cosmology and short-baseline data
In this paper we revisit the question of the information which cosmology
provides on the scenarios with sterile neutrinos invoked to describe the SBL
anomalies using Bayesian statistical tests. We perform an analysis of the
cosmological data in CDM cosmologies for different
cosmological data combinations, and obtain the marginalized cosmological
likelihood in terms of the two relevant parameters, the sterile neutrino mass
and its contribution to the energy density of the early Universe . We then present an analysis to quantify at which level a model with one
sterile neutrino is (dis)favoured with respect to a model with only three
active neutrinos, using results from both short-baseline experiments and
cosmology. We study the dependence of the results on the cosmological data
considered, in particular on the inclusion of the recent BICEP2 results and the
SZ cluster data from the Planck mission. We find that only when the cluster
data is included the model with one extra sterile neutrino can become more
favoured that the model with only the three active ones provided the sterile
neutrino contribution to radiation density is suppressed with respect to the
fully thermalized scenario. We have also quantified the level of
(in)compatibility between the sterile neutrino masses implied by the
cosmological and SBL results.Comment: 23 pages, 4 figure
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